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A006591
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a(n) = Sum_{k=1..n} nearest integer to n/k (if n/k is midway between two numbers take the smaller).
(Formerly M2434)
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0
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1, 3, 5, 8, 11, 14, 17, 22, 24, 28, 33, 36, 40, 45, 48, 53, 57, 62, 66, 71, 74, 79, 86, 89, 93, 99, 102, 109, 114, 117, 122, 129, 133, 138, 143, 148, 152, 159, 164, 169, 175, 178, 185, 190, 193, 202, 207, 212, 215, 223, 227, 232, 241, 244, 249, 256, 259, 266, 273
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OFFSET
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1,2
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COMMENTS
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Number of ways the numbers from 1..n divide the numbers from n..2n-1, n>=2. - Wesley Ivan Hurt, Feb 08 2022
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = n^2 - Sum_{k=1..n} Sum_{i=n..2n-1} sign(i mod k). - Wesley Ivan Hurt, Feb 08 2022
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EXAMPLE
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a(3) = 3 + 1 + 1 = 5. a(7) = 17 = 7 + 3 + 2 + 2 + 1 + 1 + 1.
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MATHEMATICA
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rnd[n_] := If[Mod[n, 1] > .5, Ceiling[n], Floor[n]]; Table[ Sum[ rnd[ n/k], {k, 1, n} ], {n, 1, 70} ]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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